# Level Set method for two-phase flow, how does it compare with the Volume of Fluid (VOF) method?

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 Solution Number: 1025 Title: Level Set method for two-phase flow, how does it compare with the Volume of Fluid (VOF) method? Platform: All Platforms Applies to: CFD Module, Microfluidics Module Versions: All versions Categories: Solver Keywords:

## Problem Description

I am new to COMSOL Multiphysics and have seen that you can use the Level Set method to track phase boundaries, for example in a rising bubble. I have heard of the Volume of Fluid method (VOF) before. What is the difference between the two? And what about Lagrangian methods?

## Solution

The main difference between level set methods and volume of fluid methods is that volume of fluid methods use a discontinuous function (zero in one phase and one in the other) while level set methods represent the interface by a certain contour of a smooth function. Each of these methods has one main advantage and disadvantage: Due to the discontinuity in VOF methods, it can suffer poor accuracy in the determination of the position of the interface and the calculation of the mean curvature, which in turn determines the surface tension force. The advantage is that the mass of each fluid is exactly conserved. Level set methods, on the other hand, use a smooth function, making it possible to get results with better accuracy.

In the original level set method, a signed distance function is used (that is, in each point, the level set function is the closest distance to the interface, with positive or negative sign depending on in which fluid the point is. The zero contour gives the interface). The main drawback of the originally proposed level set method is that mass is not conserved, and significant mass loss may occur. However, in COMSOL Multiphysics, we use a modified version of the level set method, which has significantly better conservation properties. It is in essence a compromise between the original level set method and the VOF method, with high order accuracy, and with good mass conservation. For an example using the Level Set method, see the Inkjet Printer Head model.

Inkjet nozzle

Concerning Lagrangian methods, where the interface is explicitly tracked, either using marker particles or a moving mesh, the main disadvantage is that they cannot handle topological changes or large deformations of the interface very well. It is also more difficult to account for surface tension forces. However, when they are applicable, highly accurate calculations can be made. In COMSOL, the Lagrangian interface tracking method available is to use a deforming mesh (ALE), see the sloshing tank example.

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